grow up (v.)

Old English growan (of plants) "to flourish, increase, develop, get bigger" (class VII strong verb; past tense greow, past participle growen), from Proto-Germanic *gro- (source also of Old Norse groa "to grow" (of vegetation), Old Frisian groia, Dutch groeien, Old High German gruoen), from PIE root *ghre- "to grow, become green" (see grass). Applied in Middle English to human beings (c. 1300) and animals (early 15c.) and their parts, supplanting Old English weaxan (see wax (v.)) in the general sense of "to increase." Transitive sense "cause to grow" is from 1774. To grow on "gain in the estimation of" is from 1712.

Have you ever heard anything about God, Topsy? ... Do you know who made you?" "Nobody, as I knows on," said the child. ... "I spect I grow'd. Don't think nobody never made me." [Harriet B. Stowe, "Uncle Tom's Cabin," 1851]

Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."

As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.

"mature," late 14c., past-participle adjective from grow up. The noun meaning "adult person" is from 1813, short for grown-up person, etc.